JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Magnetic Effects of Current

A square loop of side 2 a and carrying current I is kept in

x z

plane with its centre at origin. A long wire carrying the same current I is placed parallel to z -axis and passing through point (

0, b, 0

), (

b ≫ a

). The magnitude of torque on the loop about

z

-axis will be

Answer: (B)

Solution

The straight wire sets up a field of magnitude

B = \frac{μ _{0} I}{2 π a ^{2} + b ^{2}}

at the two sides of the loop that run parallel to it, each of length

2 a

. The force on each such side is

F = I B (2 a) = \frac{μ _{0} I ^{2} a}{π a ^{2} + b ^{2}}

. These two forces act at a perpendicular distance

a cos θ

from the

z

-axis, where

cos θ = \frac{b}{a ^{2} + b ^{2}}

, so the torque about that axis is

τ = 2 F a cos θ = \frac{2 μ _{0} I ^{2} a ^{2} b}{π ( a ^{2} + b ^{2} )}

JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Single correct option